Magnetism in zigzag graphene nanoribbons (GNRs) has received enormous attention recently, due to the one-dimensional nature of this phenomenon, as well as its potential applications in the field of spintronics. In this work, we present a density functional theory (DFT) investigation of H-passivated GNRs on the (111) surface of the topological insulator Sb2Te3. We show that the chemical interaction between the GNR and the substrate is weak. As a result, the GNR-surface distance is large, of the order of 3.4 Angstrom, doping effects are almost negligible, and the mean-field magnetic properties of the GNR are preserved. Nevertheless, the presence of the substrate affects significantly the magnitude of the exchange coupling constants between the edges. Although our DFT calculations do not properly describe quantum fluctuations that destabilize the edge magnetism in free-standing GNRs, they provide important information about the stabilizing mechanisms which originate from the substrate-induced spin orbit coupling and the decoherence effects due to the surface states of Sb2Te3. We argue that, owing to these mechanisms, Sb2Te3 may be a suitable substrate to investigate experimentally the transition from "quantum" to "classical" magnetism in GNRs.